cos^3(t) = -cos (t)

Question

Find all solutions on the interval [0,2pi) 

Please help and show steps!!

 

Thank you! 

Answer 1

Hi Anna,

 

There are two answers to this: π/2 and 3π/2

 

cos³t = -cos t

 

As you add cos t to both sides, you will get:

 

cos³t + cos t = 0

 

From here, you can factor cos t from both terms:

 

cos t (cos²t + 1) = 0

 

Set cos t = 0 and (cos²t + 1) = 0

 

cos t = 0 (from o to 2π) --->  t = π/2, 3π/2    Here is the image of unit circle:

 

 

 

cos²t + 1 = 0   cos²t = -1        You can't take square root of negative numbers.

 

 

Even though cos π = -1 from unit circle, it will turnout to be (-1)² + 1 = 2; not zero.  So, cos²t = -1 will not work.

 

 

Remember, cosine = x/r and sine = y/r.  In other words, cos -> x, sin -> y.

 

I hope you understood.  Good luck to you.

 

Yohan Chu   (LV  NV)